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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Algebra Ex.4

1. Find the quotient and remainder when
(a)

is dided by x+1.

(b)

is divided by 2x+1.

(c)

is divided by x-1.

(d)

is divided by x-2.

(e)

is divided by x-1.

(f)

is divided by x+3.

(g)

is divided by 2x+1.

(h)

is divided by x-2.

2. If the quotient on dividing

by x-3 is

, find a and b.

3. When

is divided by 2x+3, the quotient is

. Find a and b.

4. Find the quotient when

is divided by (a-2) and (a+3).

5. If x-3 is a factor of

, find a and also the other factors.

6. Find the GCD (Greatest Common Divisor) of

.

7. Find the GCD of (x³+1) and (x²-1).

8. Find the GCD of

and

.

9. Find the Least Common Multiple (LCM) of

.

10. Find the LCM of

and

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

jagabandhu

Member

Registered: 2007-03-30

Posts: 6

Re: Algebra Ex.4

In the question 1) just put the value of x in the dividend to find the remainder

e.g if you are deviding the polynomial by x+1 then just make x+1=0 so that x=-1 and put the value of x i.e. -1 in place of x in the polynomial and the resulting number would be the remainder.

To find the quotient one may divide the polynomial by the given linear polynomial or may follow the principle of factorisation.

To find the values of a and b one has to follow the factorization by using the remainder theorem as well as the factorization theorem.

To find the GCD one has to factorise the polynomials and then find the common terms.

To find the LCM one has to first factorise the terms and then take the common terms and also the other terms which are not common and multiply to get the LCM.

harman23

Member

Registered: 2007-05-26

Posts: 2

Re: Algebra Ex.4

1)

a) quotient =

    remainder=-2

b) quotient =

    remainder=-8

c) quotient =

    remainder=0

d) quotient =

    remainder=27

e) quotient =

    remainder=-6

f) quotient =

    remainder=24

g) it is same as (b)

a) quotient =

    remainder=0

harman23

Member

Registered: 2007-05-26

Posts: 2

Re: Algebra Ex.4

2)
on dividing

by  (x-3)
we will get quotient=

on compairing with given quotient

=

a=9 and b=6